The landscape law for tight binding Hamiltonians
Mathematical Physics
2022-09-14 v2 Analysis of PDEs
math.MP
Spectral Theory
Abstract
The present paper extends the landscape theory pioneered in [FM, ADFJM2, DFM] to the tight-binding Schr\"odinger operator on . In particular, we establish upper and lower bounds for the integrated density of states in terms of the counting function based upon the localization landscape.
Cite
@article{arxiv.2101.03282,
title = {The landscape law for tight binding Hamiltonians},
author = {Douglas N. Arnold and Marcel Filoche and Svitlana Mayboroda and Wei Wang and Shiwen Zhang},
journal= {arXiv preprint arXiv:2101.03282},
year = {2022}
}